When I was CX Diamond (aka OW Emerald) flying Vueling on a BA codeshare my carry on was literally thrown out of the jetway down to the tarmac, just after I reminded the cabin crew it contained fragile items and that I preferred it not to be checked in.
That said and as stated above without a OW codeshare you are not getting OW benefits, but as per my experience I don't really there are benefits at all a part from some lounge access.